Forward-central two-particle correlations in p-Pb collisions at \(\sqrt{s_{\rm NN}}\) = 5.02 TeV

.ALICE Collaboration

a r t i c l e i n f o a b s t ra c t

Articlehistory:

Received15July2015

Receivedinrevisedform30November2015 Accepted4December2015

Availableonline8December2015 Editor:L.Rolandi

Two-particle angularcorrelationsbetweentriggerparticlesintheforwardpseudorapidityrange(2.5<

|η|<4.0)andassociatedparticlesinthecentralrange (|η|<1.0)aremeasuredwiththeALICEdetector in p–Pb collisions at anucleon–nucleon centre-of-mass energy of5.02 TeV. The trigger particlesare reconstructedusingthemuonspectrometer,andtheassociatedparticlesbythecentralbarreltracking detectors. Inhigh-multiplicityevents,thedouble-ridge structure,previouslydiscovered intwo-particle angularcorrelationsatmidrapidity,isfoundtopersisttothepseudorapidityrangesstudiedinthisLetter.

The second-orderFouriercoefficientsfor muonsinhigh-multiplicityevents are extractedafter jet-like correlations fromlow-multiplicity events have been subtracted. The coefficients are found to have a similar transverse momentum (pT) dependenceinp-going (p–Pb)and Pb-going(Pb–p)configurations, withthePb-goingcoefficientslargerbyabout16±^6%,ratherindependentofpTwithintheuncertainties ofthemeasurement.ThedataarecomparedwithcalculationsusingtheAMPTmodel,whichpredictsa differentpTandηdependencethanobservedinthedata.Theresultsaresensitivetotheparentparticle v2andcompositionofreconstructedmuontracks,wherethecontributionfromheavyflavourdecaysis expectedtodominateatpT>2 GeV/c.

©^{2015CERNforthebenefitoftheALICE}Collaboration.PublishedbyElsevierB.V.Thisisanopen accessarticleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP³.

1. Introduction

Measurementsof correlationsin

ϕ

and

η

,where

ϕ

and

η

are the differences in azimuthal angle (

ϕ

) and pseudora- pidity (

η

) betweentwo particles, respectively, provide insighton the underlying mechanism ofparticle production in collisions of hadronsandnucleiathighenergy.

For such measurements in proton–proton (pp) collisions, jet production leads to a characteristic peak-like structure on the

“near side” (at

ϕ

≈^0,

η

≈^{0) and an elongated structure in}

η

onthe“away side”(at

ϕ

≈

π

)[1].Innucleus–nucleus (A–A) collisions, ridge-likestructuresextendingover along rangealong the

η

axisemergeonthenearandawaysides,inadditiontothe jet-related correlations [2–14]. The Fourierdecomposition of the correlation in

ϕ

atlarge

η

is dominatedby the second- and third-order harmonic coefficients v2 and v3, butsignificant har- monicshavebeenmeasureduptov6 [6,7,9–16].InA–Acollisions, thevncoefficientsareinterpretedasthecollectiveresponseofthe created matter to the collision geometry and fluctuationsin the initialstate[17,18],andareusedtoextractitstransportproperties inhydrodynamicmodels[19–21].

E-mailaddress:[email protected].

Long-range ridge structures on the near side (

ϕ

≈^{0) were} alsoobservedinhigh-multiplicityppcollisionsatacentre-of-mass energy √

s=^{7 TeV [22] and in} proton–lead (p–Pb) collisions at a nucleon–nucleoncentre-of-mass energy √

s_NN=⁵.02 TeV [23].

Shortly after, measurements in which the contributions fromjet fragmentation were suppressed by subtracting the correlations extracted from low-multiplicity events revealed the presence of essentially the same long-range structures on the away side as on the nearside in high-multiplicity events [24,25]. Evidence of long-range double-ridgestructures inhigh-multiplicity deuteron–

gold (d–Au) collisions at √

s_NN=⁰.2 TeV was alsoreported [26].

Bynow,theexistenceoflong-rangecorrelationsinp–Pbcollisions is firmlyestablished bymeasurements [27–31] involvingfour,six ormoreparticlecorrelations,withthelower-ordercorrelationsre- moved [32], demonstrating that the long-range ridges originate from genuine multi-particle correlations. Intriguingly, the trans- verse momentumdependenceoftheextracted v_n [27,28,30],and theparticle-massdependenceofvn [33–35]arefoundtobequal- itativelysimilartothosemeasuredinA–Acollisions.

The similarity of the ridges in the pp, p–Pb, d–Au and A–A systemssuggeststhepossibilityofacommonhydrodynamicalori- gin[36–43].However,whetherhydrodynamicalmodelscanindeed be reliably applied to such small systems is under intense de- bate[44].Otherproposedmechanismsinvolveinitial-stateeffects, such asgluonsaturation andextendedcolorconnections forming http://dx.doi.org/10.1016/j.physletb.2015.12.010

0370-2693/©^{2015CERNforthebenefitoftheALICE}Collaboration.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP³.

along the longitudinal direction [45–49] or final-state parton–

partoninducedinteractions[50–54].

Furtherinsight into theproduction mechanismof theselong- range correlation structures may be gained by studying their

η

-dependence.A preliminaryresult[55]indicatesamild

η

depen- dence,butthemeasurement islimitedto|

η

_|<2.A similarmag- nitudeofthetwo-particle correlationamplitudesin theAu-going andd-going directions at 2.8<|

η

|<3.8 has also beenreported ind–Au collisions at√

sNN=⁰.2 TeV [56]. Calculationsfor v2 at large

η

(2.5<|

η

_|<4)inp–Pbcollisions at√

sNN=⁵.02 TeV from a3+1 dimensional,viscous hydrodynamical modelandamulti- phase transport model (AMPT) predict a stronger

η

dependence, withabout50%and30%largerv2 valuesontheleadnucleusside forthehydrodynamicalandAMPTmodel,respectively[57].

InthisLetter,wereportameasurementofangularcorrelations betweentriggerparticles inthe pseudorapidityrange 2.5<|

η

|<

4.0 andassociatedparticlesinthecentralrange|

η

|<1.0 inp–Pb collisionsat√

sNN=⁵.02 TeV attheLargeHadronCollider (LHC).

Thetriggerparticles areinclusivemuons, reconstructedusingthe ALICEmuonspectrometer,andtheassociatedparticlesarecharged particles,reconstructedbytheALICEcentralbarreltrackingdetec- tors.Asinpreviousmeasurements[24,33],thedoubleridgeisex- tractedbysubtractingthecorrelationsobtainedinlow-multiplicity eventsfromthoseinhigh-multiplicityevents.Resultsforthesec- ond order Fourier coefficient for muons, vμ

2{^2PC,sub}^{, and the} ratioof vμ

2{^2PC,sub} ^{coefficients1 in the} Pb-going (Pb–p) andp- going (p–Pb)directions are reported for high-multiplicity events, andcompared tomodel predictions. The remainder ofthe Letter is structured as follows: We describe the experimental setup in Sec.2,theeventandtrackselectioninSec.3,theanalysismethod in Sec. 4 and the evaluation of the systematic uncertainties in Sec.5.Finally,inSec.6we reporttheresults,andcomparethem withmodelpredictions.InSec.7weconcludewithasummary.

2. Experimentalsetup

In 2013, the LHC provided collisions between protons with a beam energy of 4 TeV and lead ions with a beam energy of 1.58 TeV per nucleon, resulting in a centre-of-mass energy of

√sNN=⁵.02 TeV. Thebeams were set up in two configurations:

aperiodwiththeprotonmomentuminthedirectionofnegative

η

intheALICEcoordinatesystem,denotedasp–Pb,followedbyape- riodwithreversedbeams,denotedasPb–p.Duetotheasymmetric beamenergies,thenucleon–nucleoncentre-of-massreferencesys- temmoveswitharapidityof0.465inthedirectionoftheproton beamwith respect to the ALICE laboratory system. Pseudorapid- ity,denotedby

η

,isgiveninthelaboratoryframethroughoutthis Letter.

DetailsonALICEanditssubdetectorscanbefoundinRefs.[58, 59].Inthefollowing,wegiveabriefsummaryofthecomponents neededforthemeasurementreportedintheLetter.

Triggertracks used in this analysisare detected in the muon spectrometerwith an acceptanceof −⁴.0<

η

<−².5. The muon spectrometerconsistsofathick absorberofaboutteninteraction lengths(λI), whichfiltersmuonsinfront offivetrackingstations madeoftwoplanesofCathodePadChamberseach.Thethirdsta- tionisplacedinsideadipolemagnetwitha3 Tmintegratedfield.

Thetrackingapparatusiscompleted by atriggersystemmadeof four layers of Resistive Plate Chambers placed behind a second absorber of7.2λI thickness. Thissetup ensures that most ofthe

1 Here,andinthefollowing,“2PC”standsfor“two-particlecorrelation”and“sub”

for“subtraction”,andindicatestheanalysistechniquewithwhichthecoefficients aremeasured.

hadronsintheacceptancearestoppedinoneoftheabsorberlay- ers,providingamuonpurityabove99%forthetracksusedinthis analysis.Inp–Pbcollisions,thetriggerparticletravelsinthesame directionasthepbeam (p-goingcase),whileinPb–p collisionsin thesamedirectionasthePbnucleus (Pb-goingcase).

Associated particles in |

η

_|<1.0 are reconstructed using the combined information from the Inner Tracking System (ITS) and the TimeProjectionChamber (TPC), whichare located inside the ALICE solenoidwith a field of 0.5 T. The ITS consistsof six lay- ersofsilicondetectors:two layersofSiliconPixelDetector(SPD), surroundedby twolayers ofSiliconDriftDetector(SDD) andtwo layersofSiliconStripDetector(SSD).SPDtracklets,shorttrackseg- mentsreconstructedinthetwoSPDlayersalone,arealsousedas associatedparticles.

The V0 detector, consisting of two arrayswith 32 scintillator tilesarrangedinfourringseach,isusedtogeneratetheminimum- bias trigger and offline for multiplicity selection [60]. The de- tector covers the full azimuth within 2.8<

η

<5.1 (V0-A) and

−³.7<

η

<−¹.7 (V0-C).Thetiming informationoftheV0 isalso usedforofflinerejectionofinteractionsofthebeamwithresidual gas.Inaddition,twoneutronZeroDegreeCalorimeters (ZDCs)lo- catedat+¹¹².5 m (ZNA)and−¹¹².5 m (ZNC)fromtheinteraction pointare usedintheofflineeventselection andasanalternative approachtodefineevent-multiplicityclasses.

3. Eventandtrackselection

The online event selection used in this analysis is based on a combination of minimum-bias (MB) and muon trigger inputs.

The MB selection uses thecoincidence betweenhits inthe V0-A andV0-C detectors andcovers99.2% ofthenon-single-diffractive cross section as described in [61]. Only approximately 5% of the MBeventscontainone ormoretracksreconstructed inthemuon spectrometer.Inordertoincreasethenumberofrecordedevents, the presence of at least one muon above a pT threshold was required in addition to the MB trigger condition. Two different thresholdswere used:alow-pT thresholdcorresponding toabout 0.5 GeV/c (

μ

-low-pT) and a higher pT threshold corresponding to about 4.2 GeV/c (

μ

-high-p_T). These thresholds are not sharp and the reported values correspond to a 50% trigger probability for a muon candidate. The integrated luminosity collected with

μ

-high-p_T triggers is 5.0nb⁻¹ in the p–Pband 5.8 nb⁻¹ in the Pb–p periods.The

μ

-low-pTtriggerclasswasdownscaledbyafac- tor10–35dependingonthedatatakingconditions,resultinginan integratedluminosityof0.28nb⁻¹ inthep–Pband0.26nb⁻¹ in thePb–p periods.

TheTPC andSDDdetectorshavelongerdeadtimecomparedto themuonspectrometer,theSPDandtheV0.Therefore,theywere readoutonlyinafractionof

μ

-low-p_Tevents (about25%inp–Pb and below 10% in Pb–p collisions). Both muon-track andmuon- trackletcorrelation resultswere measuredin thep–Pbconfigura- tion.ForPb–p collisions,onlymuon-trackletcorrelationscouldbe studiedduetothesignificantlylower numberoftriggerswiththe TPCinthereadout.

Theprimary-vertexpositionisdetermined usingreconstructed clustersintheSPDdetectorasdescribed inRef.[59].Onlyevents with a reconstructed vertexcoordinate along the beamdirection (zvtx)within7 cmfromthenominalinteractionpointareselected.

Theprobabilityofmultipleinteractionsinthesamebunchcrossing (pileup)wasdependentonthebeamconditionsandalwaysbelow 3%.Pileupeventsareremovedbyrejectingtriggerswithmorethan onereconstructedvertex.

Alleventswerecharacterizedbytheireventactivity,andsorted intoeventclasses.As inprevious studies [24,33],the eventchar- acterizationwasbasedonthesignalintheV0 detectors.However,

Fig. 1.Parentparticlecompositionofreconstructedmuontracks(leftpanel)andreconstructionefficiencyformuonsfrompionandkaondecaysrelativetothatforheavy flavor (HF)decaymuons(rightpanel)fromadetectorsimulationoftheALICEmuonspectrometer.

Table 1

V0S multiplicity classes as fractions of the analyzed eventsampleand thecorresponding ^dNch/dη||η|<0.5. ThedNch/dηvaluesarenotcorrectedfortriggerand vertex-reconstructioninefficiencies,whichareabout4%

for non-single-diffractive events [61], mainly affecting the80–100%lowestmulitiplicityevents[62].Onlysys- tematicuncertaintiesarelisted,sincethestatisticalun- certaintiesarenegligible.

Event class

^dNch/dη||η|<0.5 pT> 0 GeV/c

0–20% 35.8±⁰.8

20–40% 23.2±⁰.5

40–60% 15.8±0.4

60–100% 6.8±0.2

unlikebefore,bothbeamorientationswereinvestigatedinthisLet- ter.Therefore,thesignalsfromonlytwooutthefourringsofV0-A andV0-C detectorswere combinedtoguaranteeamoresymmet- ricacceptance.OntheV0-A side,thetwooutermostringswithan acceptanceof 2.8<

η

<3.9, while onthe V0-C side the two in- nermostringswithanacceptanceof−³.7<

η

<−².7 were used.

ThiscombinationiscalledV0Sin thefollowing.Thedefinitionof the event classes as fractions of the analyzed event sample and their corresponding average number of particles at midrapidity (dNch/d

η

|_|η_|<0.5), measured using tracklets asexplained below, isgiveninTable 1.

Muontracksarereconstructedinthegeometricalacceptanceof themuon spectrometer(−⁴<

η

<−².5).The tracksare required toexitthefrontabsorberataradialdistancefromthebeamaxis, R_abs,intherange17.6<R_abs<89.5 cm inordertoavoidregions withlargematerialdensity.Themuon identificationisperformed by matching the tracks reconstructed in the tracking chambers with the corresponding track segments in the trigger chambers.

Beam-gastracks,whichdonotpointtotheinteractionvertex,are removedbyaselectionontheproductofthetotalmomentumofa giventrackandits distancetotheinteractionvertexinthetrans- verse plane.In theanalysis, muons inthetransverse momentum range0.5<pT<4 GeV/cwereconsidered.

Reconstructedmuonsmainlyoriginate fromweakdecaysof

π

, K² andmesonsfromheavy flavor (HF)decays.Becauseofthedif- ferent pT distribution ofthe various sources andtheabsorber in frontofthespectrometer,whichsuppressesbydesignweakdecays

2 Here,andinthefollowing,pionsandkaonsrefertothesumofbothcharge states.Neutralparticlesarealsoconsideredinthecaseofkaons.

fromlighthadrons,theparentparticlecompositionfortherecon- structedmuontrackschangesasafunctionofp_T.Thecomposition shown asa function ofthe reconstructed p_T inthe left panel of Fig. 1 was evaluated usingfulldetectorsimulations basedon the DPMJET MonteCarlo (MC) eventgenerator [63]. The detectorre- sponse was simulated using GEANT3 for particle transport [64].

The composition of parent particles in the simulation differs by lessthan10%forthetwo beamconfigurations.The reconstructed muonsaredominatedbylight-hadrondecaysbelow1.5 GeV/c,and by heavy flavor decays above 2 GeV/c. No significant multiplic- itydependencewas found.Similarconclusionsareobtainedusing simulationswiththeAMPTgenerator[65].

Without strong model assumptions, one cannot deduce the compositionofparentparticlesfromthemeasuredmuondistribu- tion,andcorrectthedataformuondecayandabsorbereffects.For comparisonofthev₂datawithcalculations,however,onlyrelative contributionsoftheparentspeciesmatter. Inordertoeasefuture modelcalculations,thereconstructionefficienciesformuonsfrom pionandkaondecaysrelativetothoseformuonsfromheavyfla- vordecaysareprovidedintherightpanelofFig. 1asafunctionof thegenerateddecaymuon pTindifferentpseudorapidityintervals.

Contributionsfrommuondecaysofotherparticlesaresignificantly smaller than those forpions andcan be ignored. The systematic uncertainty on the relative efficiencies was estimated to be less than5%.

TracksreconstructedintheITSandtheTPCareselectedinthe fiducialregion|

η

|<1 and0.5<p_T<4 GeV/c.Thetrackselection usedinthisLetteristhesameasinRef.[24].

Trackletcandidates areformed usinginformationon theposi- tionoftheprimaryvertexandthetwohitsontheSPDlayers[66], located ata distanceof3.9and7.6 cm fromthedetectorcentre.

The differences of the azimuthal (

ϕ

h, bending plane) and po- lar (θh, non-bending direction) angles ofthe hitswith respect to the primary vertexare used to selectparticles, typically with pT>50 MeV/c. Particles below 50 MeV/c are mostly absorbed by material.Compared to previous analyses [61,66] a tighter cut in

ϕ

h isapplied(

ϕ

h<5 mrad)toselectparticleswithlarger p_T andtominimizecontributionsoffakeandsecondary tracksto below 2.5%.Thecorrespondingmeanp_T ofselectedparticles,esti- matedfromtheDPMJETMC,isabout0.75 GeV/c.

4. Analysis

Theassociatedyieldoftracksortrackletspertriggerparticlein themuonspectrometerismeasuredasafunctionofthedifference

Fig. 2.Associatedyieldpertriggerparticleasafunctionofηandϕformuon-trackcorrelationsinp–Pb (left)andmuon-trackletcorrelationsinp–Pb (middle)and Pb–p (rightpanels),measuredin60–100%(toprow)and0–20%(bottomrow)eventclasses.Thetriggerparticle(muon)rangeis0.5<p^t_T<1 GeV/c,theassociatedparticle intervalsare0.5<p^a_T<4.0 GeV/cfortracksand0< ϕh<5 mrad fortracklets.Statisticaluncertaintiesarenotshown.

inazimuthalangle(

ϕ

) andpseudorapidity (

η

).As inprevious analyses[24,33],itisdefinedas

Y

=

¹ N_trig

d²N_assoc d

η

d

ϕ ⁼

S

( η , ϕ )

B

( η , ϕ ) ,

(1)

in intervals of event multiplicity and trigger particle transverse momentum, p^t_T. The variable Ntrig denotes the total number of triggerparticles in theeventclass and p^t_T interval, not corrected for single-muon efficiency. The signal distribution S(

η

,

ϕ

)= 1/N_trigd²Nsame/d

η

d

ϕ

is the associated yield per trigger par- ticle for particle pairs from the same event, obtained in 1 cm- wide intervals of zvtx. A correctionfor pair acceptance and pair efficiencyis obtainedby dividing by the background distribution B(

η

,

ϕ

)=

α

d²N_mixed/d

η

d

ϕ

. The background distribution isconstructedbycorrelatingtriggerparticlesfromoneeventwith theassociatedparticles fromother eventswithin thesame event multiplicityclassand1 cm-widezvtxintervals.Thefactor

α

isused tonormalizethebackgrounddistributiontounityinthe

η

region ofmaximalpairacceptance.Thefinalper-triggeryieldisobtained bycalculatingtheaverageoverthezvtxintervalsweightedbyN_trig. In Fig. 2, the associated yield per trigger particle as a func- tion of

ϕ

and

η

for muon-track correlations in p–Pb (left) andmuon-trackletcorrelations inp–Pb (middle) and Pb–p (right panels),measuredin60–100%(toprow)and0–20%(bottomrow) event classes is shown. In the low-multiplicity class (60–100%), the dominant feature is the recoil jet on the away side (

π

/2<

ϕ

<3

π

/2). While in previous two-particle correlation studies at midrapidity [24,33] the away-side jet structure was mostly flat in

η

, from

η

_{= −}1.5 to

η

_{= −}5.0 it decreases, as ex- pectedconsideringthe kinematicsofdijetsatlarge

η

.The near side (|

ϕ

_|<

π

/2) shows almost no structure in

ϕ

and

η

, since it is sufficiently separated from the near-side jet peak at

(

ϕ

,

η

)=(0,0),so that no contributionfrom jetsis expected.

Inthe high-multiplicity(0–20%)class, theaway-side jetstructure is also visible, and the associated yields are considerably higher thanforthelow-multiplicity(60–100%)class.Moreover,incontrast to thelow-multiplicityclass,a near-side structureemerges, simi- lartothatpreviouslyobservedatlowerpseudorapidities,revealing that the near-side ridge extends up to pseudorapidity ranges of 2.5<|

η

|<4.

Inorder toisolate long-rangecorrelations, weapply the same subtraction method as in previous measurements [24,33]. Jet- associated yields haveonly a weak multiplicity dependence[67], thus the subtraction of the low-multiplicity event class removes most of the jet-like correlations. The per-trigger yield of the 60–100% event class is subtracted from that in the 0–20% event class,andtheresultispresented (labelledasYsub)inthetoppan- elsofFig. 3.Aftersubtraction,twosimilarridgesonthenearand ontheawaysideareclearlyvisible.

The magnitude of the contributing long-range amplitudes is quantifiedbyextractingtheFouriercoefficientsfromthe

ϕ

pro- jectionoftheper-triggeryielddistribution,afterthesubtractionof thelow-multiplicityclass,asshowninthelower panelsofFig. 3.

In orderto reduce the statisticalfluctuationsatthe edges of the per-triggeryield distribution,the

ϕ

projection isobtainedfrom afirst-orderpolynomialfitalong

η

foreach

ϕ

interval.Inthe p–Pb cases,the near- and away-side amplitudesare quite differ- ent,whileinthePb–p case theamplitudesonthenearandaway sidearesimilar.Thedifferenceintheamplitudesofthenear- and away-sideridge,whichmaybeduetoaresidualjetcontributionin thesubtracteddistribution,istakenintoaccountinthesystematic errorevaluation,asexplainedinSec.5.

TheFouriercoefficientsarethenobtainedbyfittingY_subwith a0

+

^2a1cos

( ϕ ) +

^2a2cos

(

2

ϕ ) +

^2a3cos

(

3

ϕ ) ,

(2)

Fig. 3.Toppanels:Associatedyieldpertriggerparticleasafunctionofϕandηformuon-trackcorrelationsinp–Pb(left)andmuon-trackletcorrelationsinp–Pb(centre) andPb–p (right)collisionsforthe0–20%eventclass,wherethecorrespondingcorrelationfromthe60–100%eventclasshasbeensubtracted.Statisticaluncertaintiesarenot shown.Thetriggerparticle(muon)rangeis0.5<p^t_T<1 GeV/c,theassociatedparticleintervalsare0.5<p^a_T<4.0 GeV/cfortracksand0< ϕh<5 mradfortracklets.

Bottompanels:Thesameasaboveprojectedontoϕ.Thelinesindicatethefittothedataandthefirstharmoniccontributionsasexplainedinthetext.

Table 2

Summaryofmainsystematicuncertainties.TheuncertaintiesusuallydependonpTandvarywithinthegivenranges.

Systematiceffect Assoc. tracks Assoc. tracklets

p–Pb p–Pb Pb–p Ratio

Acceptance (zvtxdependence) 3–4% 0–5% 0–3% 0–1%

Remaining jet after subtraction 4–10% 5–14% 1–2% 3–15%

Remaining ridge in low-multiplicity class 1–4% 1–6% 0–2% 2–8%

Calculation ofv2 0–1% 0–1% 1% 0–2%

Resolution correction 1% 0–1% 0–1% 0–2%

Sum (added in quadrature) 7–11% 6–14% 2–4% 5–17%

leadingto

χ

²/NDF valuestypicallybelow1.5.Therelativemodu- lationisgivenby Vn{^2PC,sub}=_a0^a₊ⁿ_b^{,wherebisthebaselineof} the low-multiplicity class (60–100%) estimated from the integral ofthe per-triggeryield around the minimum.Assuming that the two-particleFouriercoefficient factorizesintoaproductoftrigger andassociatesingle-particle v₂ [30],the v_n{^2PC,sub}^coefficients forparticlesreconstructedinthemuonspectrometer arethenob- tainedas

v_n

{

^2PC

,

sub

} =

^Vn

{

^2PC

,

sub

}/

V_n^c

{

^2PC

,

sub

},

⁽³⁾

where V_n^c{^2PC,sub}^ismeasuredby correlatingonlycentralbar- reltracks(or tracklets)witheach other (essentiallyrepeatingthe analysisasinRef.[24]).

InthisLetter, v2{^2PC,sub}^{valuesformuonsintheacceptance} of the muon spectrometer are reported. Weak decays and scat- tering in the absorber of the muon spectrometer can cause the kinematicsofreconstructedmuonstodeviate fromthoseoftheir parentparticles,andcaninfluencethereconstructedv₂,especially in case v2,parent has a strong pT dependence. Since we cannot correct the measured v₂ for thespecies-dependent inefficiencies

induced by the absorber, we denote the resulting coefficientsby vμ

2{^2PC,sub} ^{to indicate that the result holds for decay muons} measuredinthemuonspectrometer.

5. Systematicuncertainties

The systematicuncertainty on vμ

2{^2PC,sub} ^{was estimated by} varying the analysis procedure as described in this section. The uncertaintyontheratiobetweenthevμ

2{^2PC,sub}^{inPb–p andp–}

Pbcollisionswas obtainedon theratioitself,inordertoproperly treatthe(anti-)correlatedsystematicsbetweenthep–PbandPb–p datasamples.A summaryisgiveninTable 2.

TheacceptanceoftheALICEcentralbarreldependsonthepo- sition ofzvtx.Tostudyits influenceon vμ

2{2PC,sub},theanalysis was repeatedusingonlyeventswithareconstructedprimaryver- texwithin ±5 cm insteadof±^{7 cm fromthenominal}interaction point. The yield per trigger particle was not corrected for sin- gle track acceptance and efficiency of associated particles. Since vμ

2{^2PC,sub}^{isarelativequantity,itisnotexpectedtodependon} thenormalization.Thiswasverifiedinthecaseofthemuon-track

analysis, where goodagreement was found betweenthe second- orderFourier coefficientsobtained withandwithout single-track acceptanceandefficiencycorrections.Hence, noadditionaluncer- taintywasconsidered.

Asobservedinpreviousanalyses[24,33],thesubtractionofthe low-multiplicityclassleadstoaresidualpeakaround(

η

,

ϕ

)≈ (0,0), possibly due to a bias of the event selection on the jet fragmentationinlow-multiplicityevents[67].The pseudorapidity gap[24,25]usedtocalculateV_n^c was variedfrom1.2 to1.0 and to0.8 in orderto estimatethe contributionofthe residualnear- sideshort-rangecorrelations.Duetothelargegapinpseudorapid- itybetweenthe ALICEcentral barrelandthemuon spectrometer, this contribution does not affect the forward-central correlation.

Theeffectofthebiasintroducedbythemultiplicityselectionwas addressedon the away side by scaling the 60–100% multiplicity class. The scaling factor (f) is determined as the ratio between away-side yields in high- and low-multiplicity classes after the subtractionofthesecond-orderFouriercomponent[67].Thispro- cedure was appliedin thecalculation ofboth Vn and V_n^c.The scaling factors were found to be larger in the caseof p–Pb col- lisions (f ≤¹.40), compared to Pb–p (f≤¹.26), and tend to be lower forincreasing pT. Thedifference withrespect to thebase- lineresults,forwhichnoscaling(f=^{1) isapplied,was takenas} thesystematicuncertainty.

Aspreviouslyreported[67],thecontributionofthelong-range correlations to the measured yields is not significant in low- multiplicity events. Still, their potential influence was addressed bychanging themultiplicity rangefrom60–100% to70–100%for thelow-multiplicityclass.

Totestthestabilityofthefit,the v2 coefficientwascalculated usinga fitwithonlythefirstandthesecond Fouriercomponents inEq.(2).Asanothervariation,thebaselinebwascalculatedfrom afit ofthe per-triggeryield in thelow-multiplicityclass using a Gaussiantomodeltheshapeoftheaway-sideridgeandaconstant to estimate b. An equivalent approach, which makes use of the baselineofthehigh-multiplicityclass B in V_n{^2PC,sub}=^an/B, wasalso used,where B was estimatedfromthe integralor from a parabolic fit of the correlation function around the minimum.

Finally, the

ϕ

projection was obtained from a weighted aver- ageinsteadofa first-orderpolynomial fitalong

η

foreach

ϕ

interval.

The effect from the finite angular and momentum resolution ofthemuon spectrometeron vμ

2{^2PC,sub} ^{wasevaluated froma} dedicatedMC studywith themeasured v2 asinput distribution, andresultedinasmallcorrectionofbelow 2%.Theassociatedun- certainty was evaluated by varying the input v₂ by 50% at the lowestandhighestmeasuredpoints.

6. Results The vμ

2{^2PC,sub} ^{coefficientswere measured formuon tracks} inthep-goingdirection(p–Pbperiod)usingbothtracksandtrack- lets as associated central barrel particles, as described in Sec. 4.

The vμ

2{^2PC,sub}^{coefficientsobtainedfromthe}per-triggeryields ofassociatedcentralbarreltracksagreewell withthoseofassoci- atedtracklets,asshowninFig. 4asafunctionofmuon pT.Since thetwomeasurements probedifferentrangesinassociatedparti- clepT,theagreementisaconsequenceoftriggerandassociatev2 factorization[30].Inaddition,goodagreementwasfoundbetween the vμ

2{^2PC,sub} ^{obtainedwithdifferent cutson}

ϕ

h ofassoci- atedtracklets (inducingachangeofaveragepTbyabout20%).

The p-going and Pb-going vμ

2{^2PC,sub} ^{coefficients obtained} usingmuon-trackletcorrelations forthetwo differentbeamcon- figurations (p–PbandPb–p)arereportedintheleftpanelofFig. 5 asafunctionofmuon p_T.ThePb-goingvμ

2{^2PC,sub}^(i.e.whenthe

Fig. 4.Comparisonofv^μ₂{^2PC,sub}^for−⁴<η<−².5 extractedfrommuon-track andmuon-trackletcorrelationsinp–Pbcollisionsat√

sNN=⁵.02 TeV.

muon triggerparticletravelsinthe samedirectionasthePbnu- cleus)isobservedtobelargerthanthep-going vμ

2{^2PC,sub}^over themeasuredpTrange,butthetwohaveasimilarpT-dependence.

Toquantifytheasymmetry,thePb-goingoverp-goingratioforthe vμ

2{^2PC,sub} ^{coefficients is reported in the right panel of Fig. 5} as a function of muon pT. The ratio is found to be ratherinde- pendent of pT given the statistical and systematic uncertainties of the measurement. A constant fit to the ratio adding statisti- cal and systematicuncertainties in quadrature gives 1.16±⁰.06 with a

χ

²/NDF=⁰.4. The analysis was also repeatedusing the energy deposited in the neutron ZDCs on the Pb-going side in- stead oftheV0S amplitude fortheeventclass definition.Asdis- cussed in detail in [62], the correlation betweenforward energy measured intheZDCsandparticledensityatcentralrapiditiesis weak inp–Pbcollisions. Therefore, eventclassesdefinedasfixed fractions of the signal distribution in the ZDCs select different events, with different mean particle multiplicity at midrapidity, than thesamples selectedwiththe samefractions inthe V0 de- tector. Still,the vμ

2{^2PC,sub}^{valuesweremeasured tobesimilar,} within25%ofthoseextractedwithV0Sestimator.Inaddition,the asymmetry between Pb- and p-going vμ

2{^2PC,sub} ^{was found to} persist with similar shape and magnitude. The observed asym- metry mayresultfromdecorrelationsofeventplanesatdifferent rapidity[68].

The data in Fig. 5 cannot be readily compared with existing predictions [57] fora 3+1 dimensional, viscous hydrodynamical model[39] andthe AMPT modelwiththestring-melting mecha- nism enabled[65]. Themodelcalculationswere performedwith- outtakingintoaccounttheeffectofthemuon absorber,andrep- resentthev2 ofprimaryparticles,whileasdiscussedinSec.3the measured vμ

2{^2PC,sub}^{coefficientsare reportedfordecaymuons.}

Dependingon particlecomposition andonthe pT-dependenceof theparentparticlev2 distribution,thedifferencebetweenprimary particlev2 anddecaymuon v2canbequitelarge.Forexample,at 1 GeV/c,assumingthev₂oftheparentparticlesriseswithp_T like atmid-rapidity [33],the measured vμ

2{^2PC,sub}^{for muonsorig-} inating fromdecaysof pions (kaons)wouldbe ≈²⁰ (40)% larger thanthatoftheparentpions (kaons).

Instead,inFig. 5weshowacomparisonofthedatawithAMPT model calculations performed with the same parameters as in [57].Thesecalculationswere performedatgeneratorlevel,decay- ing primary particles into muonsusingthe PYTHIAdecayer[69].

The effects ofthe muon absorber were includedby applying the pT and

η

dependent relative efficiencies provided in the right panelofFig. 1.Eventcharacterizationwasdonebymimickingthe V0S criteriaatparticlelevel, i.e.by countingchargedparticles in

Fig. 5.Thev^μ₂{2PC,sub}coefficientsfrommuon-trackletcorrelationsinp-goingandPb-goingdirections(left)andtheirratio(right)for−4<η<−2.5 inp–Pbcollisionsat

√sNN=5.02 TeV.ThedataarecomparedtomodelcalculationsfromAMPT.

2.8<

η

<3.9 and−³.7<

η

<−².7.The v2 valueswere obtained separatelyformuonsdecayingfrompions,kaonsandheavy-flavor hadrons, andotherwiseperforming the analysisinthesame way asindata.We foundthe v₂ forHF muonstobe consistent with zerowithinthegeneratedstatistics(5MeventswithaHFmuonin theacceptanceofthemuonspectrometerforeachperiod).Hence, for the inclusive v2, which is obtained by weighting the calcu- lated v2 with the relative yields in each decay channel, the v2 for HF muonshas been set to zero to reduce statistical fluctua- tions.InAMPTthefactor f usedtoscalelow-multiplicityclassto eliminatetheremainingjetcontributionaftersubtraction, reaches values much larger than in the data, up to f =^{2. Applying the} scalingreducestheextractedv2andconsequentlythischoicecon- stitutesthelower (upper) boundoftheshaded area inFig. 5left (right), while the opposite boundscorrespond to f =^{1 (asused} forthebaselineresultinthedata).

As shown in the left panel of Fig. 5, below pT<1.5 GeV/c, where the inclusivemuon yield is expected to be dominated by weak decays of pions and kaons, the calculation produces qual- itatively similar trends as observed in the data. However, quan- titatively a different pT and

η

dependence is found, visible in particularintherightpanel ofFig. 5.At pT>2 GeV/c,wherethe inclusivemuonyieldisdominatedbyheavy-flavordecays,thedata maysupportafinitevalueforthev2 ofHFmuons,oradrastically different composition of the parent distribution or their v₂ val- uesinAMPT compared todata.Indeed, comparingpredictions of AMPT to pion,kaon and D-meson yields measured at midrapid- ity[70,71], muonsfromheavy-flavor decays wouldbe underesti- matedbya factor3–5relative topionandkaondecaysassuming thesame discrepancybetweenmodelanddataatforwardrapid- ity.A finite value forHF muon v₂ wouldbe consistent withthe emergence of radial flow in heavy-flavor meson spectra as pre- dictedin[72],andhasbeenrecentlymeasuredinPb–Pb collisions at√

sNN=².76 TeV[73].

7. Summary

Two-particle angular correlations between trigger particles in the forward pseudorapidity range 2.5<|

η

|<4.0 and associated particles in the central range |

η

|<1.0 measured by ALICE are reported in p–Pb collisions ata nucleon–nucleon centre-of-mass energyof5.02 TeV.The triggerparticlesare inclusivemuonsand the associated particles are charged particles, reconstructed by the muon spectrometer andcentral barrel tracking detectors,re- spectively. The composition of parent particles for the measured

muons is expected to vary as a function of pT (Fig. 1). A near- side ridge is observed in high-multiplicity events (Fig. 2). After subtraction of jet-like correlations measured in low-multiplicity events, the double-ridge structure, previously discovered in two- particleangularcorrelationsatmidrapidity,isfoundtopersisteven in the pseudorapidity ranges studied here (Fig. 3). The second- order Fourier coefficients for muon tracks are determined as- suming factorization of the Fourier coefficients at central and forward rapidity. The measurement in p–Pb collisions was per- formed in two differentways, usingtracks ortracklets forparti- cles at |

η

_|<1.0, yielding consistent results (Fig. 4). The second- order Fourier coefficients for muons in high-multiplicity events were found tohave a similar transverse momentum dependence in the p-going (p–Pb) and Pb-going (Pb–p) configurations, with the Pb-going coefficients larger by 16±^{6%, rather} independent of pT within the uncertainties of the measurement (Fig. 5). The results were compared with calculations using the AMPT model incorporating the effects of the muon absorber, showing a dif- ferent pT and

η

dependence than observed in the data. Above 2 GeV/c, the results are sensitive to the v₂ of heavy-flavor de- caymuons.Forthcomingmodelcalculationsshouldapplytherela- tive efficiencies formuon decays frompion andkaons (provided in Fig. 1) at generator level for detailed comparison with our data. Further measurements (e.g. ofheavy-flavor muon yields or charged-particle v₂ at forward rapidity) will be needed to re- duce the ambiguity between muon parent particle composition andtheir v2.

Acknowledgements

The ALICECollaboration would like to thank all its engineers andtechniciansfortheirinvaluablecontributionstotheconstruc- tionoftheexperimentandtheCERNacceleratorteamsfortheout- standingperformanceoftheLHCcomplex.TheALICECollaboration gratefully acknowledges the resources and support provided by all Grid centresandthe WorldwideLHC ComputingGrid (WLCG) Collaboration. The ALICE Collaboration acknowledges the follow- ing funding agencies for their support in building and running the ALICEdetector:State CommitteeofScience,WorldFederation of Scientists (WFS)and Swiss Fonds Kidagan, Armenia; Conselho Nacional de Desenvolvimento Científico e Tecnológico(CNPq), Fi- nanciadora de Estudose Projetos(FINEP),Fundaçãode Amparoà Pesquisa do Estado de São Paulo (FAPESP); National Natural Sci- enceFoundation of China (NSFC),the ChineseMinistry ofEduca- tion(CMOE)andtheMinistryofScienceandTechnology ofChina (MSTC); Ministryof Education and Youth of the Czech Republic;